Qualitative Analysis for a New Integrable Two-Component Camassa–Holm System with Peakon and Weak Kink Solutions

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• 作者：Kai Yan ; Zhijun Qiao ; Zhaoyang Yin
• 刊名：Communications in Mathematical Physics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：336
• 期：2
• 页码：581-617
• 全文大小：456 KB
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• 作者单位：Kai Yan (1)
  Zhijun Qiao (2)
  Zhaoyang Yin (1) (3)
  
  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, Guangdong, China
  2. Department of Mathematics, University of Texas-Pan American, Edinburg, TX, 78541, USA
  3. Faculty of Information Technology, Macau University of Science and Technology, Macau, China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Quantum Physics
  Quantum Computing, Information and Physics
  Complexity
  Statistical Physics
  Relativity and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0916

文摘

This paper is devoted to a new integrable two-component Camassa–Holm system with peaked solitons (peakons) and weak-kink solutions. It is the first integrable system that admits weak kink and kink–peakon interactional solutions. In addition, the new system includes both standard (quadratic) and cubic Camassa–Holm equations as two special cases. In the paper, we first establish the local well-posedness for the Cauchy problem of the system, and then derive a precise blow-up scenario and a new blow-up result for strong solutions to the system with both quadratic and cubic nonlinearity. Furthermore, its peakon and weak kink solutions are discussed as well.